Cite

[1] Birman, V., Byrd, L.W. Modeling and analysis of functionally graded materials and structures. Applied mechanics reviews (2007) 60: 195-216.10.1115/1.2777164Search in Google Scholar

[2] Ying, J., Lu, C.F., Chen, W.Q. Two -dimensional elasticity solutions for functionally graded beams resting on elastic foundation. Composite Structures (2008) 84: 209-219.10.1016/j.compstruct.2007.07.004Search in Google Scholar

[3] Benatta, M.A, Mechab, I., Tounsi, A., Adda Bedia, E.A. Static analysis of functionally graded short beams including warping and shear deformation effects. Computational Materials Science (2008)44: 765-773.10.1016/j.commatsci.2008.05.020Search in Google Scholar

[4] Kadoli, R., Akhtar, K., Ganesan, N. Static analysis of functionally graded beams using high order shear deformation theory. Applied Mathematical Modelling (2008) 32: 2509-252510.1016/j.apm.2007.09.015Search in Google Scholar

[5] Giunta, G., Belouettar, S., Carrera, E. Analysis of FGM Beams by Means of Classical and Advanced Theories. Mechanics of Advanced Materials and Structures (2010) 17: 622-635.10.1080/15376494.2010.518930Search in Google Scholar

[6] Kang. Y.A., Li, X.F. Large Deflections of a Non-linear Cantilever Functionally Graded Beam. Journal of Reinforced Plastics and Composites (2010) 29: 1761-1774.10.1177/0731684409103340Search in Google Scholar

[7] Huang, Y., Li, X.F. Buckling Analysis of Nonuniform and Axially Graded Columns with Varying Flexural Rigidity. Journal of Engineering Mechanics - ASCE (2011) 137: 73-81.10.1061/(ASCE)EM.1943-7889.0000206Search in Google Scholar

[8] Asghari, M., Rahaeifard, M., Kahrobaiyan M.H., Ahmadian, M.T. The modified couple stress functionally graded Timoshenko beam formulation. Material and Design (2011) 32: 1435-144310.1016/j.matdes.2010.08.046Search in Google Scholar

[9] Kocaturk, T., Simsek, M., Akbas, S.D. Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material. Science and Engineering of Composite Materials (2011) 18: 21-34.10.1515/secm.2011.005Search in Google Scholar

[10] Mohanty, C.S., Dash, R.R., Rout, T. Parametric instability of a functionally graded Timoshenko beam on Winkler’s elastic foundation. Nuclear Engineering and Design (2011) 241: 2698-2715.10.1016/j.nucengdes.2011.05.040Search in Google Scholar

[11] Ma. L.S., Lee, D.W. Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading. European Journal of Mechanics A/Solids (2012) 31: 13-20.10.1016/j.euromechsol.2011.06.016Search in Google Scholar

[12] Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M., Bedia, E.A.A. Analytical Solutions for Static Shear Correction Factor of Functionally Graded Rectangular Beams. Mechanics of Advanced Materials and Structures (2012) 19: 641-652.10.1080/15376494.2011.581409Search in Google Scholar

[13] Zhou, Li, S.R., Wan, Z.Q., Zhang, P. Relationship between Bending Solutions of FGM Timoshenko Beams and Those of Homogenous Euler-Bernoulli Beams. Applied Mechanics and Materials: Progress in Structures, PTS 1-4 (2012) 166-169: 2831-2836.Search in Google Scholar

[14] Soleimani, A., Saadatfar, M. Numerical Study of Large Deflection of Functionally Graded Beam with geometry Nonlinearity. Advanced Material Research: MEMS, Nano and Smart Systems, PTS 1-6 (2012) 403-408: 4226-4230Search in Google Scholar

[15] Birsan, M., Altenbach, H., Sadowski, T., Eremeyev, V.A., Pietras, D. deformation analysis of functionally graded beams by the direct approach. Composites: Part B (2012) 43: 1315-132810.1016/j.compositesb.2011.09.003Search in Google Scholar

[16] Mohanty, S.C., Dash, R.R., Rout, T. Static and Dynamic Stability of Functionally Graded Timoshenko Beam. International Journal of Structural Stability and Dynamics (2012) 12.10.1142/S0219455412500253Search in Google Scholar

[17] Zhao, L., Chen, W.Q., Lu, C.F. Symplectic elasticity for bi-directional functionally graded materials. Mechanics of Materials (2012) 54: 32-42.10.1016/j.mechmat.2012.06.001Search in Google Scholar

[18] Esfahani, S.E., Kiani, Y., Eslami, M.R. Non-linear stability thermal analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations. International Journal of Mechanical Science (2013) 69: 10-2010.1016/j.ijmecsci.2013.01.007Search in Google Scholar

[19] Ansari, R., Gholami, R., Faghih Shojaei, M., Mohammadi, V., Sahmani, S. Size-dependent bending, buckling and free vibration of functionally graded Timoshenko nicrobeams based on the most general strain gradient theory. Composite Structure (2013) 100: 385-397.10.1016/j.compstruct.2012.12.048Search in Google Scholar

[20] Zhang, Da-Guang. Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Composite Structures (2013) 100: 121-126.10.1016/j.compstruct.2012.12.024Search in Google Scholar

[21] Li, S.R., Cao, D.F, Wan, Z.Q. Bending solutions of FGM Timoshenko beams from those of the homogenous Euler-Bernoulli beams. Applied Mathematical Modelling (2013) 37: 7077-7085.10.1016/j.apm.2013.02.047Search in Google Scholar

[22] Zamanzadeh M., Rezazadeh G., Jafarsadeghi-poornaki, I., Shabani, R. Static and dynamic stability modeling of a capacitive FGM micro-beam in presence of temperature changes. Applied Mathematical Modelling (2013) 37: 6964-6978.10.1016/j.apm.2013.02.034Search in Google Scholar

[23] Mao, Y.Q., Ai, S.G., Fang, D.N., Fu, Y.M, Chen, C.P. Elasto-plastic analysis of micro FGM beam basing on mechanism-based strain gradient plasticity theory. Composite Structures (2013) 101: 168-179.10.1016/j.compstruct.2013.01.027Search in Google Scholar

[24] Abbasnejad, B., Rezazadeh, G., Shabani, R. Stability Analysis of a Capacitive FGM Micro-Beam using Modified Couple Stress Theory. ACTA Mechanica Solida Sinica (2013) 26: 427-440.10.1016/S0894-9166(13)60038-5Search in Google Scholar

[25] Akgoz, B., Civalek, O. Buckling analysis of functionally graded microbeams based on the strain gradient theory. Acta Mechanica (2013) 224: 2185-2201.10.1007/s00707-013-0883-5Search in Google Scholar

[26] Zhang, B., He, Y., Liu, D., Gan, Z., Shen, L. A novel size-dependent functionally graded curved microbeam model based on the strain gradient elasticity theory. Composite Structures (2013) 106: 374-392.10.1016/j.compstruct.2013.06.025Search in Google Scholar

[27] Zhang. D.G. Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Meccanica (2014) 49: 283-293. 10.1007/s11012-013-9793-9Search in Google Scholar

[28] Li, Y.L., Meguid, S.A., Fu, Y.M., Xu, D.L. Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam. Proceedings of the Royal Society a Mathematical Physical and Engineering sciences (2014) 470.10.1098/rspa.2013.0473389605924511250Search in Google Scholar

[29] Shen H-S., Wang, Z-X. Nonlinear analysis of shear deformable FGM beams resting on elastic foundation in thermal environments. International Journal of Mechanical Sciences (2014) 81: 195-206.10.1016/j.ijmecsci.2014.02.020Search in Google Scholar

[30] Hadji, L., Daouadji, T.H., Tounsi, A., Bedia, E.A. A higher order shear deformation theory for static and free vibration of FGM beam. Steel and Composite Structures (2014) 16: 507-519.10.12989/scs.2014.16.5.507Search in Google Scholar

[31] Nguyen, D.K., Gan, B.S., Trinh, T.H. Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material. Structural Engineering and Mechanics (2014) 49: 727-743.10.12989/sem.2014.49.6.727Search in Google Scholar

[32] Zhang. D.G., Zhou, H.M. Nonlinear Bending and Thermal Post-Buckling Analysis of FGM Beams Resting on Nonlinear Elastic Foundation. CMES - Computer Modelling in Engineering & Science (2014) 100: 201-222.Search in Google Scholar

[33] Sitar. M., Kosel, F., Brojan, M. Large deflections of nonlinearly elastic functionally graded composite beams. Archives of Civil and Mechanical Engineering (2014) 14: 700-709.10.1016/j.acme.2013.11.007Search in Google Scholar

[34] Cai, K., Gao, D.Y., Qin, Q.H. Postbuckling analysis of a nonlinear beam with axial functionally graded material. Journal of Engineering Mathematics (2014) 88: 121-136.10.1007/s10665-013-9682-1Search in Google Scholar

[35] Chu, P., Li, X.-F., Wang, Z.-G., Lee, K.Y. Double cantilever beam model for functionally graded materials based on two-dimensional theory of elasticity. Engineering Fracture Mechanics (2015) 135: 232-244.10.1016/j.engfracmech.2015.01.008Search in Google Scholar

[36] Filippi, M., Carrera, E., Zenkour, A.M. Static analyses of FGM beams by various theories and finite elements. Composites: Part B (2015) 72: 1-9.10.1016/j.compositesb.2014.12.004Search in Google Scholar

[37] Chakraborty, A., Gopalakrishnan, S., Reddy, J.N. A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences (2003) 45: 519-539.10.1016/S0020-7403(03)00058-4Search in Google Scholar

[38] Alshorbagy A.E., Eltaher, M.A., Mahmoud F.F. Free vibration characteristics of a functionally graded beam by finite element. Applied Mathematical Modelling (2011) 35: 412-425.10.1016/j.apm.2010.07.006Search in Google Scholar

[39] Murin, J., Aminbaghai M., Kutis, V. Exact solution of the bending vibration problem of the FGM beam with variation of material properties. Engineering Structures (2010) 32: 1631-1640.10.1016/j.engstruct.2010.02.010Search in Google Scholar

[40] Aminbaghai, M., Murin, J., Kutis V. Modal analysis of the FGM-beams with continuous transversal symmetric and longitudinal variation of material properties with effect of large axial force. Engineering Structures (2012)34: 314-329.10.1016/j.engstruct.2011.09.022Search in Google Scholar

[41] Murin, J., Aminbaghai, M., Kutis, V., Hrabovsky, J. Modal analysis of the FGM beams with effect of axial force under longitudinal variable elastic Winkler foundation. Engineering Structures (2013) 49: 234-247.10.1016/j.engstruct.2012.09.039Search in Google Scholar

[42] Murin, J., Aminbaghai, M., Hrabovsky, J., Kutis, V., Kugler St. Modal analysis of the FGM beams with effect of the shear correction function. Composites: Part B (2013) 45:1575-1582.10.1016/j.compositesb.2012.09.084Search in Google Scholar

[43] Kutis, V., Murin, J., Belak, R., Paulech, J. Beam element with spatial variation of material properties for multiphysics analysis of functionally graded materials. Computers and Structures (2011)89: 1192 - 1205.10.1016/j.compstruc.2010.10.012Search in Google Scholar

[44] Rubin, H. Analytische Berechnung von Stäben und Stabwerken mit stetiger Veränderlichkeit von Querschnitt, elastischer Bettung und Massenbelegung nach Theorie erster und zweiter Ordnung, Baustatik - Baupraxis 7. Berichte der 7. Fachtagung "Baustatik - Baupraxis" Aachen/Deutschland 18.-19. März 1999. Balkema 1999, Abb., Tab.S.135-145.Search in Google Scholar

[45] Rubin, H. Solution of differential equations of arbitrary order with polynomial coefficients and application to a statics problem ZAMM (1996)76: 105-117.Search in Google Scholar

[46] S. Wolfram MATHEMATICA 5, Wolfram research, Inc., 2003.Search in Google Scholar

[47] Altenbach, H., Altenbach, J., Kissing, W. Mechanics of composite structural elements. Springer Verlag, (2003). 10.1007/978-3-662-08589-9Search in Google Scholar

[48] Halpin, J.C., Kardos, J.L. The Halpin-Tsai equations. A review, Polymer Engineering and Science. (1976) 16: 344-352.10.1002/pen.760160512Search in Google Scholar

[49] Reuter, T., Dvorak, G.J. Micromechanical models for graded composite materials: Ii.Thermomechanical loading. J. of the Mechanics and Physics of Solids (1998) 46:1655-1673.10.1016/S0022-5096(97)00039-2Search in Google Scholar

[50] Murin, J., Kutis, V. Improved mixture rules for composite (FGMs) sandwich beam finite element.In Computational Plasticity IX. Fundamentals and Applications. Barcelona, Spain, (2007): 647-650.Search in Google Scholar

[51] Alshorbagy, A.E., Eltaher, M.A., Mahmoud F.F. Free vibration of a functionally graded beam by finite element method. Applied Mathematical Modelling (2010) 35: 412 - 425.10.1016/j.apm.2010.07.006Search in Google Scholar

[52] Simsek, M. Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite Structures (2010) 92: 904-917.10.1016/j.compstruct.2009.09.030Search in Google Scholar

[53] Rout, T. On the dynamic stability of functionally graded material under parametric excitation.PhD thesis. National Institute of Technology Rourkela, India. (2012).Search in Google Scholar

[54] Kutis, V., Murin, J., Belak, R., Paulech, J. Beam element with spatial variation of material properties for multiphysics analysis of functionally graded materials. Computers and Structures (2010) 89: 1192-1205.10.1016/j.compstruc.2010.10.012Search in Google Scholar

[55] Murin, J., Kugler, S., Aminbaghai, M., Hrabovsky, J., Kutis, V., Paulech, J. Homogenization of material properties of the FGM beam and shells finite elements. In.: 11th World Congress on Computational mechanics (WCCM XI), Barcelona, 2014.Search in Google Scholar

[56] Murin, J., Aminbaghai, M., Hrabovsky, J., Kutis, V., Paulech, J., Kugler, S. A new FGM beam finite element for modal analysis. In.: 11th World Congress on Computational mechanics (WCCM XI), Barcelona, 2014.Search in Google Scholar

[57] Murin, J., Kugler, S., Aminbaghai, M., Hrabovsky, J., Kutis, V., Paulech, J. Homogenization of material properties of the FGM beam and shell finite elements. In.: 11th World Congress on Computational mechanics (WCCM XI), Barcelona, 2014.Search in Google Scholar

[58] Murín, J., Hrabovský, J., Kutiš, V., Paulech, J.Shear correction function derivation for the FGM beams. In: 2nd International Conference on Multi-scale Computational Methods for solid and Fluids. 10. 6- 12. 6.2015, Sarajevo, Bosnia and Hercegovina, (2015).Search in Google Scholar

[59] Murin, J., Aminbaghai, M., Hrabovsky, J., Kutis, V. Kugler, S. Effect of the Shear Correction Function in the FGM Beams Modal Analysis. In Proceedings of the 15th European Conference on Composite Materials. 24-28 June 2012, Venice, Italy, (2012) ISBN 978-88-88785-33-2.Search in Google Scholar

[60] ANSYS Swanson Analysis System, Inc., 201 Johnson Road, Houston, PA 15342/1300, USA. Search in Google Scholar

eISSN:
2450-5471
Language:
English
Publication timeframe:
2 times per year
Journal Subjects:
Engineering, Mechanical Engineering, Fundamentals of Mechanical Engineering, Mechanics